## The Annals of Statistics

### On the Asymptotic Equivalence of Two Ranking Methods for $K$-Sample Linear Rank Statistics

#### Abstract

Two methods of ranking $K$ samples for rank tests comparing $K$ populations are considered. The first method ranks the $K$ samples jointly; the second ranks the $K$ samples pairwise. These procedures were first suggested by Dunn (1964), and Steel (1960), respectively. It is shown that both ranking procedures are asymptotically equivalent for rank-sum tests satisfying certain nonrestrictive conditions. The problem is formulated in terms of multiple comparisons, but is applicable to other nonparametric procedures based on $K$-sample rank statistics.

#### Article information

Source
Ann. Statist., Volume 5, Number 6 (1977), 1099-1106.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343998

Digital Object Identifier
doi:10.1214/aos/1176343998

Mathematical Reviews number (MathSciNet)
MR518897

Zentralblatt MATH identifier
0391.62053

JSTOR
Koziol, James A.; Reid, Nancy. On the Asymptotic Equivalence of Two Ranking Methods for $K$-Sample Linear Rank Statistics. Ann. Statist. 5 (1977), no. 6, 1099--1106. doi:10.1214/aos/1176343998. https://projecteuclid.org/euclid.aos/1176343998